Abstract High intensity focused ultrasound (HIFU) has been heavily investigated over the past two decades for treating a wide range of diseases and medical conditions. As a non-invasive surgical modality that can reach deep tissues, HIFU has the potential to revolutionize therapy. A versatile and fast yet sufficiently accurate ultrasound numerical model is vital for HIFU. Such a numerical model could serve as a powerful platform for in-depth investigation of HIFU and as a springboard for clinical translation of HIFU techniques. Some specific applications include testing new sonication protocols, understanding the mechanism of certain HIFU techniques, and rapid treatment planning. Two common HIFU techniques exist: they are the thermal based HIFU technique and shock wave based HIFU technique. While the first type uses relatively low pressure continuous wave (CW) and primarily causes thermal coagulation, the second type uses high pressure shock wave pulses to cause mechanical fractionation of tissue. To this date, no model can efficiently and accurately model these two types of HIFU in three-dimensional (3D) large-scale, complex, heterogeneous biological tissue. In the proposed research, we shall address a longstanding need in the HIFU community for a novel, accuracy- efficiency balanced numerical model. In Aim 1, we shall create a versatile, accuracy-efficiency balanced algorithm for HIFU modeling. By considering tissue heterogeneities in the Westervelt equation, a modified wave- vector-frequency-domain (M-WVFD) method for predicting linear/nonlinear wave fields in arbitrarily heterogeneous media will be systematically investigated for the first time. The resulting model is expected to be at least two orders of magnitude faster than the state-of-the-art ?accurate? models and still have high accuracy. In Aim 2, the M-WVFD method will be numerically and experimentally validated by investigating a variety of HIFU problems. The experiments will involve both phantom and ex-vivo human skulls in order to investigate wave propagation in weakly and strongly heterogeneous media. Aim 3 shall focus on software engineering, so that the developed algorithms can be integrated into an open-source software package and can be widely adopted by the HIFU community.